From 859059fb9d38d7662a061c68554c216e891de1f8 Mon Sep 17 00:00:00 2001 From: Daira Hopwood Date: Mon, 11 Apr 2016 22:14:15 +0100 Subject: [PATCH] Add note about Merkle tree validity. Signed-off-by: Daira Hopwood --- protocol/protocol.pdf | Bin 808092 -> 808242 bytes protocol/protocol.tex | 3 +++ 2 files changed, 3 insertions(+) diff --git a/protocol/protocol.pdf b/protocol/protocol.pdf index 4551142b75c99739af26ac8afc83621978e29bf1..a7bc7a946eb854a7f2c8a00ab6616323f72c8931 100644 GIT binary patch delta 63789 zcmV(~K+nINsWGyuF_2P!-*4MC5Pr{Jp+^~*IQ|y-*rd(24s8R(*no9=U?n;hDodUu zcMY&Ven*j#WyhJbt!o`G|z^wyr6qA|YT_x0MX;1BoXoIL#I&RCRajkuQJ zK#j!E``VhycRsJjzF}&A`kBq0kByVxmUT0X)b!4J*NZ3WGJb8kr3q;KT$CA@Rq@9| zULo+#7=h&wBr*3BdbVzg(pw_rn*i$8A9}|hu<20BVM$zngOGU(7qAx?aX9vm*7xKz z(nw3U?gapmP`6FPE+Vr;QxX3F9cbJ&wHr0gH`%ZgBd!&qDIEZ0-k*bX#}@UrF3jfN z^k$)V-B0C%`>}pjV645@8aPHwmX~nFV1p=t8f+^aG!d+mU`pLW0h7+&0CSv+8IRA4 z&b=_$5WjDKY?aw|M&i(Bs@%7|sPe*8m2H7AlIR%C5`po(53Y}@Jgo zq|5BOJIFGAlw|>MK9cOpamK@pIc| zO|cG5R8yJ8>Og5Vj5i^?7z-<$tET=bl_~L-@>h&lBjSQR@@w#j6zz`Xrgy289s5%uJ?{&LbSgdn+6XtR(7v!^S%u6qw(RR4yW*c zhnWzuDT^F7B#3WelX8Bl_&zgWcps^4)>I`cQB|6TGV#^mYT zl%~pnN~umyNzG$kk0=0*;3KpW$BU8u5^%SOhtvB+o&N|z_!K46NsbU|$B=Dob0V)P zCz=8S4M)waXtK?qx07`+f~XdQ-U#O>)o|V|`fo6&IQq}9B|FlwmC)YtQNl2iEFHcI zPIX_*&;A0o4nRe-@C2p^0yiL+u}TRjf9;q{Q`;~Q$M1X!ALWCM^|GuZErg*RW*A5> zr9B8+Njx}mMt0if+gFNg=Rv}w0~7{dVre~*Wc{_jU2Wuzy~sN~h??i8;lbg6AdiPU zMzJ>>d6akzu@ExT%e-q4`vFH3oT=bOsLT&=fW5GIrjpXgqSxoh0qURgb+AUsb0*MBL+O8AoK$oMQ{5- zIDZ%G-1RU5btl5R4id}(M4Q&gNtJY3p+>7?xzY+_3~qdsfQ4-nAe`w^rui(F%D$=X zocO(O*sC3ZZDmOGurjz&=5slne>R&gv{5ACs6Xy6^+mgc!W-5t&IXW#oDeTSMm&m~ zc+A1p@UJwkgA82N*dh1Gx7|$3s*;r>Z-?Wra#8I>FMcd~S%==CZwAytRWqSGkF`#G zVcWt-3@oP7hd|k8^X|yLTP+SoFz)gEq{Ff8#jNA&enE8p%cn6AwRE&ye;$K?5&prM z`4YNxvb1o$&}A*tT4p=EV_l^!*PsygxZV3j|Kca45#(y-8() z=I+GZ-Dz1EOzqFD1S;+0cay&m9Uk5x))u^3WJCmq5w1g0=!sufXx%j0%i{*q!= z)T@MYx@?Np{xF=LAePbYhx=PQHvST#kjna(+-&!&1m3gOFMGS{KHcYKWhZ%87Vq6G z%9}+}glX2zl2@D9n^Ket-i_H6yMuX^exY3Mw~=+Q6cO3aidG3v>GIo{rWBHbbpzWv zubO<_miy|2a!9}6va#!bs`jn^K$h=ToG-nj%4a zr2McitDg?rvJ)6nf2_bLmAD(bF6;HN9~nr%C?YBKA(~Lhmp|5e4>4Ft6H!QlLEbFQ z771ZU5oUk%6&-ObF)2Rj=WvR%x%@9s(->;E6QTQ3RVz4RWj* zZ#R+o^e`BacmwT!(oRfE1X2JZZ+O)ibU3d-LND8&w|0AcW9_!Rw_gde0L7qey~ALP zRAu%z-`XL*QNh=;YTCS7yXkra>3Wx2OO{)y4!NLx8xy$Q+kKN)9$Jpxus7%T3C(reW z-a~YMpS{YYk3PaVq5!Id0BK3pDTAj@BoBJ{XdLHk|SoNeaG87$q>Lgv0SBCLACdLI{ddl7+%` zrVt3k5g&9iMF7m$4DwR(_Hg7OF;|};my!x zHg6+qg~)B{r=!{=2Z)0f(gqGPD!a+#@WoojCVGip@3b7PO+Zl;wR)N5Y*SGelph__1m!|D)V^=`+wEQt zd0$p{_R)G@ZA#sUa4G6N@M_E$L7^1FO82I}7xmjMOv+MhlSBBF0*VAPMbxr?T~V_9 z7~?5eAs+0%v5OL*}D}Nw)8)(%}9)Y2%%HS!j6fidlob^VcJb`=thUWA%j?e6x}Q2$EyaF34M~z{+iUIAH+Y!t1@`-t{mJXq8|gm%?>_oNnuVSLM!p z-6-%QJ>s=Eo*+{`l>mLhrrtWBw!m9IO8zsBJ(15bs9hVM4m2wc>ZjK>! zrxOkS&I!~-5!;T`mO?uhw|A|x2yzJq^PeH}(#Ht&@chuYa_En>KF?Zx7&6*SA~YrG`CxH0^0USUt!ZA)ZKY&>jq>VVij21|MzJ*q$`O7{`ll0rCF`Kxr40RQ|G??> zB|mRg5^$T)AydL3oN;#guhH<(^B@XBL6!&9Gp%d*)y-@u4ZVz3@3a7Z0CK9C1gQ^m zhY09}ZDB~CH<;zzxfB=5GGLIpMoWV=1d;((hBFFtgqqXlnqWl`?Zi37F|155!ujeG2bMoot*{eu*EFBej-Ebxw@;uTWPpPIlIt9`1&Qk+Eq;er~BkeMv< z<3C=-&NC>ZBu^$Qxot%00>`MjG8nrq+7Znk>9mK%VRy5CQ4dRczXiJ=0>&4y_>H3s zOk9{o@F=VdiWxyz`S3;7aZE|W($$=LX4HC#f>}6l8CB+hlRY7D&{4>;FtL!L%lz2h z@6VYp@S%EW>-{P#p^w#}Ic>n_ySAU!=g7v04~-g9Z?oJ!czZcFw$z5sW*fR&;AT_% zmd<`JOBd#UNL$p>M@HpYdK#q+JRq*KOwX}jYobD!Gn(2&d;hwxl3l*t7WqxNJ?mG8 zMSpc}mHe*7w}@5Z*;W}VS=mC4IsM7cxJ*zWz}Fk~xgJx6_O6W~Llmp?c0@nJj_3@J zsq55oQiwTeN9BvC%7>%LSDtMf`%4*~ZJX^cPo1QH2rX2Cg>sMt%!hEN_LwDD)7GYF%ui=xuUPgSfT$}nfh^;&ONc)71f3aE>9c_{n##Go>=+~#ek z#Rh(AZ$U!t?`1C0F17xF*-Z0c+qmgs*OLeX01kY=D|T+MDG^S}_o3!=)N4Pu;GF3$C*BK zRjzZ_>RaBf4~FtDFH)cP*PT4c>hPjt*G%xE`O@+Slb>S>@a4jqMZ>MuX1(>D)BT`M|v? 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z0s(>#`7X@XoX?S$8ekd3VA=+F=YBxG8l=lwYQO_bZdnoN!qb6Hong~F*_4T-TX%_Wj0jLIQ)oYbrWq>?J$7Nwuwx|2)&PwdkOf8+fCEt~${NJC!w>Im_4DzPl zWZN$1r5Q_6(m0q!XJ@E1M5!BoJ0+r`Y!?S_t zF50_yhGKll?)+6HOYxNg)Tj0PJz;siGF6NBZ@M8I5&_1Uk^lZtDx%2}x~`V`vqx^Zo&h$4o&gSYw?ChMd6cl3e H;;{b@c1j=W diff --git a/protocol/protocol.tex b/protocol/protocol.tex index dfb7ef49..c8bae8d4 100644 --- a/protocol/protocol.tex +++ b/protocol/protocol.tex @@ -1138,6 +1138,9 @@ for each $i \in \setofOld$ \changed{$\mid$ $\vOld{i} \neq 0$}: $\treepath{i}$ must be a valid \merklePath of depth $\MerkleDepth$, as defined in \crossref{merkle}, from $\Commitment(\cOld{i})$ to \noteCommitmentTree root $\rt$. +\textbf{Note:} Merkle path validity covers both conditions 1. (a) and 1. (d) of the NP statement +given in section 4.2 of \cite{ZerocashOakland}. + \subparagraph{Balance} $\changed{\vpubOld\; +} \vsum{i=1}{\NOld} \vOld{i} = \vpubNew + \vsum{i=1}{\NNew} \vNew{i}$.